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Paul [167]
3 years ago
14

Eighty-five percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a r

andom sample of 120 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels
Mathematics
1 answer:
Natali5045456 [20]3 years ago
3 0

Answer:

mean=102

variance=15.3

standard deviation=3.91

Step-by-step explanation:

The data depict the binomial distribution because the outcome can be categorize into one of two categories that are American who favors and American who don't favor spending Govt. money to develop alternative sources of fuel for automobiles. The trial are independent and repeated 120  times. The probability of success is American who favors that is 85%.

The mean of binomial distribution is

mean=np

Here n=120 and p=0.85

Mean for the number who favor government spending for alternative fuels

mean=120*0.85=102

The variance of binomial distribution is

variance=npq

n=120, p=0.85 and q=1-p=1-0.85=0.15

The variance for the number who favor government spending for alternative fuels

Variance=120*0.85*0.15=15.3

The standard deviation for the number who favor government spending for alternative fuels  can be found by taking the square root of variance

Standard deviation=√variance=√15.3

Rounding the value of standard deviation to two decimal places

Standard deviation=3.91

The mean, variance, and standard deviation for the number who favor government spending for alternative fuels are 102, 15.3 and 3.91 respectively.

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The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees°
Schach [20]

Answer:

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 98.6, \sigma = 0.6, n = 36, s = \frac{0.6}{\sqrt{36}} = 0.1

If 36 adults are randomly​ selected, find the probability that their mean body temperature is greater than 98.4degrees° F.

This is 1 subtracted by the pvalue of Z when X = 98.4. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{98.4 - 98.6}{0.1}

Z = -2

Z = -2 has a pvalue of 0.0228

1 - 0.0228 = 0.9772

97.72% probability that their mean body temperature is greater than 98.4degrees° F.

6 0
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Supplementary angle = 180

180 - 51 = x

x = 129

C) 129 degrees is your answer

hope this helps
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